lgx*lgy=lg(x*y)吗?求(log2 5 +log4 0.2)(log5 2+log25 0.5)急用!

lg(x*y)=lgx+lgy
log(a^2)b=1/2log(a)b
所以原式=[log(2)5+1/2*log(2)0.2][log(5)2+1/2log(5)0.5]
=1/2log(2)(10*0.2)*1/2log(5)(4*0.5)
=1/4*log(2)2log(5)2
=1/4*log(5)2